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3 years ago

How many numbers between 4000 and 5000 can be formed with the

Mathematics

1 answer:

marin [14]3 years ago

5 0

Answer:

36 numbers

Step-by-step explanation:

Number of digits in a number between 4000 and 5000 = 4

_ _ _ _

First digit of the number will be filled by 4.

So, the number of ways to fill the first digit = 1

4 _ _ _

If the given number is divisible by 5 then the last digit should be 5.

4 _ _ 5

So, the number of ways that the last digit should be 5 is = 1

Remaining 2 digits between 4 and 5 can be filled by any number given.

Therefore, number of ways that second place can be filled = 6

Similarly, number of ways that the third place of the number can be filled = 6

Now total number of ways = 1 × 6 × 6 × 1

= 36

Therefore, numbers between 4000 and 5000, divisible by 5 = 36

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The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed.

Anton [14]

Answer:

a) The evidence suggest the true mean life of a biomedical device > 5500

b) (5487.94, +∞)

c) There is evidence to support that the mean is equal to 5500

Step-by-step explanation:

Here we have

(a) To test the hypothesis we have the claim that the mean life of biomedical devices > 5500

Therefore, we put the null Hypothesis which is the proposition that a difference does not exist. That is

H₀: μ = 5500

Therefore, the alternative hypothesis will be

Hₐ: μ > 5500

The test statistic is then found by;

$t=\frac{\bar{x}-\mu }{\frac{s }{\sqrt{n}}} =\frac{5617.8-5500 }{\frac{234.5 }{\sqrt{15}}} \approx 1.95$

The P value from the T table at df = n - 1 = 15 - 1 = 14 is

0.025 < P < 0.05

The P value is given as 0.036 from the T distribution at 14 derees of freedom df

Therefore, since P < α or 0.05, we reject the null hypothesis. That is we fail to reject Hₐ: μ > 5500. The evidence suggest the true mean life of a biomedical device > 5500

(b) The 95% confidence interval is given as

$CI=\bar{x}\pm t_\alpha \frac{s}{\sqrt{n}}$

Which gives t $_\alpha$ = $\pm$ 2.145

$CI=5617.8\pm 2.145 \times \frac{234.5}{\sqrt{15}}$

The confidence interval of the lower bound on the mean is then

(5487.94, +∞)

c) From the above result, we find that the mean of 5500 is contained in the range of the lower confidence on the mean. We can therefore, accept the null hypothesis. That is there is evidence to support that the mean is equal to 5500.

6 0

3 years ago

Help X(-X^4)(-x^4)=

Kruka [31]

X(-x^4)(-x^4)=

The answer is x^9

4 0

2 years ago

10. 2x + 7y = 1 2x - 4y = 12 Solve for y

adoni [48]

Answer:

The solution for y = -1.

Step-by-step explanation:

Given:

$2x\ +\ 7y\ =\ 1$ ....(1)

$2x\ -\ 4y\ =\ 12$ ....(2)

So, to solve for y, first we solve for x in equation (2):

$2x-4y=12$

⇒ $2x=12+4y$

Dividing both sides by 2,

⇒ $x=6+2y$

Now, substituting the value of x in equation (1):

$2x+7y=1$

⇒ $2(6+2y)+7y=1$

⇒ $12+4y+7y=1$

⇒ $12+11y=1$

⇒ $11y=1-12$

⇒ $11y=-11$

Dividing both sides by 11,

⇒ $y=-1$

Therefore, the solution for y = -1.

7 0

3 years ago

Estamate 12871+6281+5146 by first rounding each number to the nearest thousand.

Pie

12,871 rounded to nearest thousand = 13,000.

6281 rounded to nearest thousand = 6,000.

5146 rounded to nearest thousand = 5,000.

In total, 13,000 + 6,000 + 5,000 = 24,000.

4 0

3 years ago

Explain the distance formula. Then use it to calculate the

Alex777 [14]

Answer:

$dAB=10\ units$

Step-by-step explanation:

we know that

The distance formula is derived by creating a triangle and using the Pythagorean theorem to find the length of the hypotenuse. The hypotenuse of the triangle is the distance between the two points

The formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$